They are different things, because for business, you can use private, public or common property, and also personal property. The type of property does not imply the type of use that can be given to it.
If I zap you bitcoins, that's a business
Yes, but this does not imply that the type of property changes. In socialism you can do small businesses with personal property, in that system what is important is your contribution to society and that your actions do not harm the rest of the community (that is why private ownership of the means of production and speculation is not allowed).
So I can sell 3d printed doodads, but not apples at the farmers market?